Since the so-called Hermite–Hadamard type inequalities for convex functions were presented, their generalizations, refinements, and variants involving various integral operators have been extensively investigated. Here we aim to establish several Hermite–Hadamard–Fejér type inequalities for symmetrized convex functions and Wright-quasi-convex functions with a weighted function symmetric with respect to the midpoint axis on the interval involving the known generalized fractional integral operators. We also point out that certain known inequalities are particular cases of the results presented here.
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This research is supported by Ordu University Scientific Research Projects Coordination Unit (BAP). Project Number: B-1809.
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This article does not contain any studies with human participants or animals performed by any of the authors.
Conflict of interest
Erhan Set declares that he has no conflict of interest. Junesang Choi declares that he has no conflict of interest. E. Aykan Alan declares that he has no conflict of interest.
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Set, E., Choi, J. & Alan, E.A. Hermite–Hadamard–Fejér type inequalities involving generalized fractional integral operators. J Anal 27, 1007–1027 (2019). https://doi.org/10.1007/s41478-018-0159-5
- Convex function
- Quasi-convex function
- Symmetrized convex function
- Wright-quasi-convex functions
- Hermite–Hadamard type inequalities
- Generalized fractional integral operators
- Hermite–Hadamard–Fejér type inequalities
Mathematics Subject Classification